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(a) The areas of two similar triangles are 36 and 25 If a median of the smaller triangle has length 10, find the length of the corresponding median of the larger (912) (b) Corresponding altitudes of two similar triangles have lengths 3 and 4 If the area of the larger triangle is 112, find the area of the smaller (c) Two similar polygons have perimeters of 32 and 24 If the area of the smaller is 27, find the area of the larger (d) The areas of two similar pentagons are 88 and 22 If a diagonal of the larger has length 5, find the length of the corresponding diagonal of the smaller (e) In two similar polygons, the ratio of the lengths of two corresponding sides is 23:1 If the area of the smaller is 15, find the area of the larger (911) (911).



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Summary

1. Angle bisector of a triangle: An angle bisector of a triangle is a segment or ray that bisects an angle and extends to the opposite side.

Thus BD, the angle bisector of /B in Fig. 1-31, bisects /B, making /1 > /2.

2. Median of a triangle: A median of a triangle is a segment from a vertex to the midpoint of the opposite side.

Fig. 1-31

Fig. 1-32

3. Perpendicular bisector of a side: A perpendicular bisector of a side of a triangle is a line that bisects and is perpendicular to a side.

4. Altitude to a side of a triangle: An altitude of a triangle is a segment from a vertex perpendicular to the opposite side.





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Accounting records are kept on the accrual basis, except in the case of very small businesses. To accrue means to collect or accumulate. This means that revenue is recognized when earned, regardless of when cash is actually collected and expense is matched to the revenue, regardless of when cash is paid out. Most revenue is earned when goods or services are delivered. At this time, title to the goods or services is transferred and a legal obligation to pay for such goods or services is created. Some revenue, such as rental income, is recognized on a time basis, and is earned when the speci ed period of time has passed. The accrual concept demands that expenses be kept in step with revenue, so that each month sees only that month s expenses applied against the revenue for that month. The neces sary matching is brought about through a type of journal entry. In this chapter, we shall discuss these adjusting entries, and also the closing en tries through which the adjusted balances are ultimately transferred to balance sheet accounts at the end of the scal year.

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Thus BD, the altitude to AC in Fig. 1-33, is perpendicular to AC and forms right angles 1 and 2. Each angle bisector, median, and altitude of a triangle extends from a vertex to the opposite side.

5. Altitudes of obtuse triangle: In an obtuse triangle, the altitude drawn to either side of the obtuse angle falls outside the triangle.

Thus in obtuse triangle ABC (shaded) in Fig. 1-34, altitudes BD and CE fall outside the triangle. In each case, a side of the obtuse angle must be extended.

Fig. 1-33

Fig. 1-34

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1.11 Naming a triangle and its parts In Fig. 1-35, name (a) an obtuse triangle, and (b) two right triangles and the hypotenuse and legs of each. (c) In Fig. 1-36, name two isosceles triangles; also name the legs, base, and vertex angle of each.

Fig. 1-35

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